An RC circuit was built as shown below: Sw Where R is the resistance in a (ohm), C is the capacitance in F (Farad). V is the voltage applied to this circuit and is given by: V = Vmax * sin (wt + g) [v] where Vmax is the maximum voltage applied, w is the angular frequency in [rad/sec] and o is the phase angle in [rad]. The switch Sw is initially open. It closes at time t = 0. When the switch is closed, a current i starts to circulate in the circuit as shown in the figure. The mathematical expression that governs the circuit's behaviour is as follows: Ri +f i dt = Vmax "sin (wt + g) (1) Answer the following questions: a) Differentiate equation (1). You should get a differential equation in the form of 4. b) Write the differential equation you obtained in part a) in its standard form. c) Obtain the general solution for i(t) of this standard form. d) Obtain the particular solution of c), knowing that i(0) = 0. Hint: You may need this: cos(wt + p) :(w·sin(wt + q) + +C a*b²w² + 1 a·b
An RC circuit was built as shown below: Sw Where R is the resistance in a (ohm), C is the capacitance in F (Farad). V is the voltage applied to this circuit and is given by: V = Vmax * sin (wt + g) [v] where Vmax is the maximum voltage applied, w is the angular frequency in [rad/sec] and o is the phase angle in [rad]. The switch Sw is initially open. It closes at time t = 0. When the switch is closed, a current i starts to circulate in the circuit as shown in the figure. The mathematical expression that governs the circuit's behaviour is as follows: Ri +f i dt = Vmax "sin (wt + g) (1) Answer the following questions: a) Differentiate equation (1). You should get a differential equation in the form of 4. b) Write the differential equation you obtained in part a) in its standard form. c) Obtain the general solution for i(t) of this standard form. d) Obtain the particular solution of c), knowing that i(0) = 0. Hint: You may need this: cos(wt + p) :(w·sin(wt + q) + +C a*b²w² + 1 a·b
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![An RC circuit was built as shown below:
Sw
R
Where R is the resistance in 2 (ohm), C is the capacitance in F (Farad). V is the voltage applied to this circuit and is given
by:
V = Vmax ' sin (wt + p) [v]
where Vmax is the maximum voltage applied, w is the angular frequency in [rad/sec] and o is the phase angle in [rad].
The switch Sw is initially open. It closes at time t = 0. When the switch is closed, a current i starts to circulate in the circuit
as shown in the figure.
The mathematical expression that governs the circuit's behaviour is as follows:
Ri +Si dt = Vmax sin (wt + 4)
(1)
Answer the following questions:
a) Differentiate equation (1). You should get a differential equation in the form of
b) Write the differential equation you obtained in part a) in its standard form.
c) Obtain the general solution for i(t) of this standard form.
d) Obtain the particular solution of c), knowing that i(0) = 0.
Hint:
You may need this:
|elab) . cos(wt + q)dt :
cos(wt + p)
+C
w. sin(wt + p) +
a?b?w? +1
a·b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd0abdad-00a1-45e7-bf48-0fc3b2f9dbef%2F4abddb4a-ed36-484a-8c63-47c652e4982c%2F77mh5dw_processed.png&w=3840&q=75)
Transcribed Image Text:An RC circuit was built as shown below:
Sw
R
Where R is the resistance in 2 (ohm), C is the capacitance in F (Farad). V is the voltage applied to this circuit and is given
by:
V = Vmax ' sin (wt + p) [v]
where Vmax is the maximum voltage applied, w is the angular frequency in [rad/sec] and o is the phase angle in [rad].
The switch Sw is initially open. It closes at time t = 0. When the switch is closed, a current i starts to circulate in the circuit
as shown in the figure.
The mathematical expression that governs the circuit's behaviour is as follows:
Ri +Si dt = Vmax sin (wt + 4)
(1)
Answer the following questions:
a) Differentiate equation (1). You should get a differential equation in the form of
b) Write the differential equation you obtained in part a) in its standard form.
c) Obtain the general solution for i(t) of this standard form.
d) Obtain the particular solution of c), knowing that i(0) = 0.
Hint:
You may need this:
|elab) . cos(wt + q)dt :
cos(wt + p)
+C
w. sin(wt + p) +
a?b?w? +1
a·b
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